The dynamic behavior of freely propagating premixed flames with large Lewis numbers was computationally simulated using a sixth-order central difference scheme and nonreflective boundary conditions. Results in the linear stage of the instability growth show that the growth rate dramatically decreases with increasing Lewis number and that the large activation energy excites the pulsating instability and increases the growth rate of the hydrodynamic instability. In the nonlinear growth stage, there exist regimes of stable cell propagation, periodic pulsating cellular flames, and irregular pulsating cellular flames as the activation energy is increased. Characteristics of these regimes were further studied for the effects of Lewis number on the flame front structure in the regime of stable cell propagation, the effects of flame pulsation on the flow and flame cell structure in the regime of periodic pulsating cellular flame, and the complex pattern formation in the regime of irregular pulsating cellular flame. It is further demonstrated that unsteady pulsating flames can propagate faster than the adiabatic flame when the local stretch rate is positive, implying that models based on quasi-steady flame propagation may not correctly predict the behavior of unsteady flames with large Lewis numbers.